calculus-max & min

posted by .

an open box with a square base is to be constructed from 48 square inches of material. What dimensions will produce a box with maximum volume?

  • calculus-max & min -

    The way I read your question:
    You have 48 square inches available in total to make the box.

    so let the base be x by x inches and the height y inches
    total area available = x^2 + 4xy = 48
    y = (48 - x^2)/(4x)

    volume = x^2 y
    = x^2 (48 - x^2)/(4x)
    = 12x - x^3/4

    d(volume)/dx = 12 - (3/4)x^2
    = 0 for a max of volume
    (3/4)x^2 = 12
    x^2 = 16
    x = √16 = 4

    if x = 4, then y = (48 - 16)/16 = 2

    the box should have a base of 4 inches by 4 inches and a height of 2 inches

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. calculus

    An open box of maximum volume is to be made from a square piece of cardboard, 24 inches on each side, by cutting equal squares from the corners and turning up the sides to make the box. (a) Express the volume V of the box as a function …
  2. calculus

    A rectangular box is to be constructed from two different materials. The box will have a square base and open top. The material for the bottom costs $4.25/m2. The material for the sides costs $2.50/m2. Find the dimensions of the box …
  3. algebra

    Make a box with a square base using only 250 square feet of material. what dimensions for the box will produce a maximum valume?
  4. algebra

    have 50 sq ft of material to make an open top box with a square base. a) use formula for surface area to express the height h of the box in terms of x. b) find the dimensions of the box that will produce the maximum volume.
  5. Physics

    An open box with a square base (see figure) is to be constructed from 160 square inches of material. The height of the box is 3 inches. What are the dimensions of the box?
  6. Calculus

    An open top bos with a square base is to be constructed from 192 sq ft of material. What should be the dimensions of the box if the volume is to be a maximum?
  7. calc

    If an open box has a square base and a volume of 91 in.3 and is constructed from a tin sheet, find the dimensions of the box, assuming a minimum amount of material is used in its construction.
  8. Calculus

    An OPEN box has a square base and a volume of 108 cubic inches and is constructed from a tin sheet. Find the dimensions of the box, assuming a minimum amount of material is used in it's construction. HINT: the goal is to minimize the …
  9. Calculus

    A rectangular box is to have a square base and a volume of 20 ft3. If the material for the base costs 37¢/square foot, the material for the sides costs 10¢/square foot, and the material for the top costs 13¢/square foot, determine …
  10. Calculus I

    An open box with square base is to be constructed. The material for the base costs $10 per square foot. The material for the sides costs $1 per square foot. the box must have an area of 100 square feet. Find the dimensions of the box …

More Similar Questions